Do Now: How do we find the value of trigonometric functions of half angles?(These formulas will be on the Regents Reference sheet)
By the end of the lesson, you will be able to...
1. discover the half angle formulas
2. verify the validity of the formula for the sine, cosine, and tangent of the angle ½x
3. apply the formulas for sin(½x), cos(½x), and tan(½x) to find the exant value of expressions involving angles measured in radians and in degrees
4. state the half angle formulas in words
Copy these questions into your notebooks. Answer them as you watch Video 1
What is the formula for sin(½x)?
What is the formula for cos(½x)?
After you watch the video, see if you can derive the formula for tan(½x).
By the end of the lesson, you will be able to...
1. discover the half angle formulas
2. verify the validity of the formula for the sine, cosine, and tangent of the angle ½x
3. apply the formulas for sin(½x), cos(½x), and tan(½x) to find the exant value of expressions involving angles measured in radians and in degrees
4. state the half angle formulas in words
Copy these questions into your notebooks. Answer them as you watch Video 1
Video 1
This video shows the application of tan(½x). It also shows tan(2x) which you learned on the last page - ignore this.
Video 2
- Classwork: If 180⁰<A<270⁰ and sin A = - sqrt5/3, find a. sin (½A), b. cos(½A), and c. tan(½A)
Answers: a. sqrt30/6, b. - sqrt6/6, and c. - sqrt5Half_Angles.JPG
A-Half_Angle.JPG